   # (a) Assume the equation x = At 3 + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B . (b) Determine the dimensions of the derivative dx / dt = 3 At 2 + B . ### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

#### Solutions

Chapter
Section ### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
Chapter 1, Problem 10P
Textbook Problem
5580 views

## (a) Assume the equation x = At3 + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt = 3At2 + B.

(a)

To determine

The dimensions of the constant A and B in the equation x=At3+Bt.

### Explanation of Solution

Write the equation of the motion of a particular object having x as function of t

x=At3+Bt                                                  (I)

Here, x is the position of the object, t is the time, A is any constant and B is any constant.

The dimension of x is L and the dimension of t is T.

Assume the dimension of A is LaTb and the dimension of B is LcTd.

Since the given equation is dimensionally correct. So, the dimension on left side must balance the dimension of right side.

Equating the dimension of x and At3.

Substitute L for x and LaTb for At3.

L=(LaTb)T3L=LaTb+3

Equating the exponent on both side of the equation,

a=1

b+3=0b=3

Substitute 1 for a and 3 for b to find the dimension of A

(b)

To determine

The dimensions of the derivative dxdt in the equation dxdt=3At2+B.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
The smallest unit of any substance is the _____. a. atom b. molecule c. cell

Biology: The Unity and Diversity of Life (MindTap Course List)

This controversy addresses accusations launched against sugars in foods and beverages as causes of health probl...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What type of remnant do the lowest-mass main-sequence stars become?

Foundations of Astronomy (MindTap Course List)

Where did the Earths heavy elements come from?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin

Draw two different Lewis diagrams of C4H6.

Introductory Chemistry: An Active Learning Approach 